Bessel beam plane illumination microscope

ABSTRACT

A microscope has a light source for generating a light beam having a wavelength, λ, and beam-forming optics configured for receiving the light beam and generating a Bessel-like beam that is directed into a sample. The beam-forming optics include an excitation objective having an axis oriented in a first direction. Imaging optics are configured for receiving light from a position within the sample that is illuminated by the Bessel-like beam and for imaging the received light on a detector. The imaging optics include a detection objective having an axis oriented in a second direction that is non-parallel to the first direction. A detector is configured for detecting signal light received by the imaging optics, and an aperture mask is positioned

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the priority of U.S. Provisional PatentApplication Nos. 61/354,532, filed Jun. 14, 2010, entitled “BESSEL BEAMPLANE ILLUMINATION MICROSCOPE”; 61/386,342, filed Sep. 24, 2010,entitled “BESSEL BEAM PLANE ILLUMINATION MICROSCOPE”; and 61/433,034,filed Jan. 14, 2011, entitled “BESSEL BEAM PLANE ILLUMINATIONMICROSCOPE.” The subject matter of each of these earlier filedapplications is hereby incorporated by reference.

TECHNICAL FIELD

This disclosure relates to microscopy and, in particular, to Bessel beamplane illumination microscopy.

BACKGROUND

Several imaging technologies are commonly used to interrogate biologicalsystems. Widefield imaging floods the specimen with light, and collectslight from the entire specimen simultaneously, although high resolutioninformation is only obtained from that portion of the sample close tothe focal plane of the imaging objective lens. Confocal microscopy usesthe objective lens to focus light within the specimen, and a pinhole ina corresponding image plane to pass to the detector only that lightcollected in the vicinity of the focus. The resulting images exhibitless out-of-focus background information on thick samples than is thecase in widefield microscopy, but at the cost of slower speed, due tothe requirement to scan the focus across the entire plane of interest.

For biological imaging, a powerful imaging modalities is fluorescence,since specific sub-cellular features of interest can be singled out forstudy by attaching fluorescent labels to one or more of theirconstituent proteins. Both widefield and confocal microscopy can takeadvantage of fluorescence contrast. One limitation of fluorescenceimaging, however, is that fluorescent molecules can be optically excitedfor only a limited period of time before they are permanentlyextinguished (i.e., “photobleach”). Not only does such bleaching limitthe amount of information that can be extracted from the specimen, itcan also contribute to photo-induced changes in specimen behavior,phototoxicity, or even cell death.

Unfortunately, both widefield and confocal microscopy excitefluorescence in every plane of the specimen, whereas the informationrich, high resolution content comes only from the vicinity of the focalplane. Thus, both widefield and confocal microscopy are very wasteful ofthe overall fluorescence budget and potentially quite damaging to livespecimens. A third approach, two photon fluorescence excitation (TPFE)microscopy, uses a nonlinear excitation process, proportional to thesquare of the incident light intensity, to restrict excitation toregions near the focus of the imaging objective. However, like confocalmicroscopy, TPFE requires scanning this focus to generate a completeimage. Furthermore, the high intensities required for TPFE can give riseto other, nonlinear mechanisms of photodamage in addition to thosepresent in the linear methods of widefield and confocal microscopy.

Thus, there is a need for the ability to: a) confine excitationpredominantly to the focal plane of imaging optics, to reducephotodamage and photobleaching, as well as to reduce out-of-focusbackground; b) use widefield detection, to obtain images rapidly; and c)can be used with linear fluorescence excitation, to avoid nonlinearphotodamage.

FIG. 1 is a schematic diagram of a light sheet microscopy (LSM) system100. As shown in FIG. 1, LSM uses a beam-forming lens 102, external toimaging optics, which include an objective 104, to illuminate theportion of a specimen in the vicinity of the focal plane 106 of theobjective. In one implementation, the lens 102 that providesillumination or excitation light to the sample is a cylindrical lensthat focuses light in only one direction, thereby providing a beam oflight 108 that creates a sheet of light coincident with the objectivefocal plane 106. A detector 110 then records the signal generated acrossthe entire illuminated plane of the specimen. Because the entire planeis illuminated at once, images can be obtained very rapidly.

In another implementation, termed Digital Laser Scanned Light SheetMicroscopy (DSLM), the lens 102 can be a circularly symmetricmulti-element excitation lens (e.g., having a low numerical aperture(NA) objective) that corrects for optical aberrations (e.g., chromaticand spherical aberrations) that are prevalent in cylindrical lenses. Theillumination beam 108 of light then is focused in two directions to forma pencil of light coincident with the focal plane 106 of the imagingobjective 104. The width of the pencil beam is proportional to the 1/NA,whereas its length is proportional to 1/(NA)². Thus, by using theillumination lens 102 at sufficiently low NA (i.e., NA<<1), the pencilbeam 108 of the excitation light can be made sufficiently long toencompass the entire length of the desired field of view (FOV). To coverthe other direction defining the lateral width of the FOV, the pencilbeam can be scanned across the focal plane (e.g., with a galvanometer,as in confocal microscopy) while the imaging detector 110 integrates thesignal that is collected by the detection optics 112 as the beam sweepsout the entire FOV.

A principal limitation of these implementations is that, due to thediffraction of light, there is a tradeoff between the XY extent of theillumination across the focal plane of the imaging objective, and thethickness of the illumination in the Z direction perpendicular to thisplane. In the coordinate system used in FIG. 1, the X direction is intothe page, the Y direction is in the direction of the illumination beam,and the Z direction is in the direction in which imaged light isreceived from the specimen.

FIG. 2 is a schematic diagram of a profile 200 of a focused beam oflight. As shown in FIG. 2, illumination light 202 of wavelength, λ, thatis focused to a minimum beam waist, 2w_(o), within the specimen willdiverge on either side of the focus, increasing in width by a factor of√{square root over (2)} in a distance of z_(R)=πw_(o) ²/λ, the so-calledRayleigh range. Table 1 shows specific values of the relationshipbetween the usable FOV, as defined by 2z_(R), and the minimum thickness2w_(o) of the illumination sheet, whether created by a cylindrical lens,or by scanning a pencil beam created by a low NA objective.

TABLE 1 2w_(O) (μm, for λ = 500 nm) 2z_(R) (μm, for λ = 500 nm) 0.2 0.060.4 0.25 0.6 0.57 0.8 1.00 1.0 1.57 2.0 6.28 5.0 39.3 10.0 157 20.0 628

From Table 1 it can be seen that, to cover FOVs larger than a fewmicrons (as would be required image even small single cells in theirentirety) the sheet thickness must be greater than the depth of focus ofthe imaging objective (typically, <1 micron). As a result, out-of-planephotobleaching and photodamage still remain (although less than inwidefield or confocal microscopy, provided that the sheet thickness isless than the specimen thickness). Furthermore, the background fromillumination outside the focal plane reduces contrast and introducesnoise which can hinder the detection of small, weakly emitting objects.Finally, with only a single image, the Z positions of objects within theimage cannot be determined to an accuracy better than the sheetthickness.

SUMMARY

In one general aspect, a microscope can include a light source forgenerating a light beam having a wavelength, λ, and beam-forming opticsconfigured for receiving the light beam and generating a Bessel-likebeam that is directed into a sample. The beam-forming optics can includean excitation objective having an axis oriented in a first direction.The microscope can include imaging optics configured for receiving lightfrom a position within the sample that is illuminated by the Bessel-likebeam and for imaging the received light on a detector. The imagingoptics can include a detection objective having an axis oriented in asecond direction that is non-parallel to the first direction. Themicroscope can also include a detector configured for detecting signallight received by the imaging optics, and an aperture mask positionedbetween the sample and the detector configured to prevent lightilluminated by side lobes of the Bessel beam from reaching the detector,while allowing light illuminated by a central lobe of the Bessel beam toreach the detector.

Implementations can include one or more of the following features. Forexample, the microscope can also include beam scanning optics that canbe configured for scanning the Bessel-like beam in a direction having acomponent perpendicular to the first direction. The microscope can alsoinclude image-positioning optics positioned in an optical path betweenthe sample and the detector, and configured for imaging signal lightfrom different positions with the sample while the Bessel-like beam isscanned by the beam scanning optics through a fixed position of theaperture mask. The aperture mask can define a slit. The detector can bea line detector.

The Bessel-like beam can have a ratio of a Rayleigh length, z_(R) to aminimum beam waist, w_(o), of more than 2πw_(o)/λ and less than100πw_(o)/λ. The Bessel-like beam can have a non-zero ratio of a minimumnumerical aperture to a maximum numerical aperture of less than 0.95.The Bessel-like beam can have a non-zero ratio of a minimum numericalaperture to a maximum numerical aperture of less than 0.90. TheBessel-like beam can have a minimum numerical aperture greater than zeroand a ratio of energy in a first side of the beam to energy in thecentral lobe of the beam of less than 0.5.

The microscope can also include a coverslip that supports the samplewhere a normal direction to a plane of the sample supports the sampleforms and angle with the first direction of more than 10 degrees andless than 80 degrees. The sample can be less than ten micrometers thick.The signal light can have a wavelength of λ/2. The signal light can begenerated through a non-linear signal generation process. The signallight can include fluorescence light emitted from the sample afterexcitation by the Bessel-like beam. The signal light can be generatedthrough a non-linear signal generation process. The microscope can alsoinclude an annular mask in a path of the light beam configured togenerate an annular ring of light from which the Bessel-like beam isformed.

In another general aspect, a microscope can include a light source forgenerating a light beam having a wavelength, λ, and beam-forming opticsconfigured for receiving the light beam and generating a Bessel-likebeam that is directed into a sample. The beam-forming optics can includean excitation objective having an axis oriented in a first direction.The microscope can include imaging optics configured for receiving lightfrom a position within the sample that is illuminated by the Bessel-likebeam and for imaging the received light on a detector. The imagingoptics can include a detection objective having an axis oriented in asecond direction that is non-parallel to the first direction. Themicroscope can also include a detector configured for detecting lightreceived by the imaging optics where the detector includes a pluralityof individual detection units. The microscope can also include acontroller operably coupled to the detector and configured toselectively record image data from individual detection units that imageportions of the sample that are illuminated by a central lobe of theBessel-like beam while not recording data from individual detectionunits that image portions of the sample that are not illuminated by thecentral lobe of the Bessel-like beam, and can also include a processorconfigured to generate an image of the sample based on the selectivelyrecorded image data that is recorded from different positions of theBessel beam within the sample.

Implementations can include one or more of the following features. Forexample, the microscope can also include beam scanning optics configuredfor scanning the Bessel-like beam within the sample in a directionhaving a component perpendicular to the first direction. The beamscanning optics can be configured to scan the Bessel-like beam in thesample in steps that are greater than or approximately equal to acorresponding spacing between neighboring individual detector elementsin the detector. The microscope can also include a beam blocking unitconfigured to block the Bessel-like beam from reaching the sample whenthe Bessel-like beam is scanned form one step position to a next stepposition.

The microscope can also include a diffractive optical element (DOE)configured to generate a plurality of light beams from the light beamgenerated by the light source. The beam-forming optics can be configuredfor receiving the plurality of light beams and generating a plurality ofBessel-like beams that in the sample. The plurality of light beams canbe spaced from each other by a spatial period that is greater than thediameter of a side lobe of the Bessel-like beams. The imaging optics canbe further configured for simultaneously receiving light from positionswithin the sample that are illuminated by the plurality of Bessel-likebeams and for imaging the received light on the detector. The controllercan be further configured to selectively record image datasimultaneously from individual detection units that image portions ofthe sample that are illuminated by a central lobe of the Bessel-likebeams while not recording data from individual detection units thatimage portions of the sample that are not illuminated by the centrallobes of the Bessel-like beams.

The processor can be configured to generate an image of the sample basedon the selectively recorded image data that is recorded from differentpositions of the Bessel beam within the sample, after the plurality ofBessel-like beams are scanned over the spatial period. The Bessel-likebeam can have a ratio of a Rayleigh length, z_(R) to a minimum beamwaist, w_(o), of more than 2πw_(o)/λ and less than 100πw_(o)/λ. TheBessel-like beam can have a non-zero ratio of a minimum numericalaperture to a maximum numerical aperture of less than 0.95. TheBessel-like beam can have a non-zero ratio of a minimum numericalaperture to a maximum numerical aperture of less than 0.90. TheBessel-like beam can have a minimum numerical aperture greater than zeroand a ratio of energy in a first side of the beam to energy in thecentral lobe of the beam of less than 0.5.

The microscope can also include a coverslip that supports the samplewhere a normal direction to a plane of the sample that supports thesample forms and angle with the first direction of more than 10 degreesand less than 80 degrees. The sample can be less than ten micrometersthick. The microscope can also include an annular mask in a path of thelight beam configured to generate an annular ring of light from whichthe Bessel-like beam is formed.

In yet another general aspect, a microscope can include a light sourcefor generating a light beam having a wavelength, λ, and beam-formingoptics, including an optical element positioned in a path of the lightbeam and configured for generating an annular ring of light. Thebeam-forming optics being configured for generating from the light beaman excitation beam having a central lobe and at least one side lobe andalso configured to direct the excitation beam to a position within asample. The beam-forming optics can include an excitation objectivehaving an axis oriented in a first direction, and a transverse profileof the excitation beam in the sample can be intermediate between aprofile of a lowest order Bessel function and the Gaussian function. Themicroscope can also include imaging optics configured for receivinglight from a position within the sample that is illuminated by theexcitation beam and for imaging the received light on a detector. Theimaging optics can include a detection objective having an axis orientedin a second direction that is non-parallel to the first direction. Themicroscope can also include a detector configured for detecting lightreceived by the imaging optics.

Implementations can include one or more of the following features. Forexample, the optical element can be positioned in a path of the lightbeam and can be configured for generating an annular ring of lightincludes an annular apodization mask. The optical element can bepositioned in a path of the light beam and can be configured forgenerating an annular ring of light includes a binary phase mask. Theoptical element can be positioned in a path of the light beam and can beconfigured for generating an annular ring of light includes aprogrammable spatial light modulator. The excitation beam can have anon-zero minimum numerical aperture and a maximum numerical aperture,and a ratio between the minimum numerical aperture and the maximumnumerical aperture can be less than about 0.95. The excitation beam canhave a non-zero minimum numerical aperture and a maximum numericalaperture, and a ratio between the minimum numerical aperture and themaximum numerical aperture can be less than about 0.90. An amount ofenergy in a highest-energy side lobe of the excitation beam can be lessthan about half of an amount of energy in the central lobe of theexcitation beam.

A ratio of a Rayleigh length, z_(R), of the excitation beam in thesample to a minimum beam waist, w_(o), of the excitation beam in thesample is more than about 2πw_(o)/λ and less than about 100πw_(o)/λ. Themicroscope can also include a cover slip having a planar surface uponwhich the sample is mounted or cultured. The planar surface can betilted at an angle between 10 and 80 degrees with respect to the firstdirection. The sample can be less than ten micrometers thick. Themicroscope can also include beam scanning optics configured for scanningthe excitation beam in a direction having a component perpendicular tothe first direction. The signal light can have a wavelength of λ/2.

In yet another general aspect, a microscope can include a light sourcefor generating a light beam having a wavelength, λ, and beam-formingoptics configured for receiving the light beam and generating aBessel-like beam that is directed into a sample. The beam-forming opticscan include an excitation objective having an axis oriented in a firstdirection. The microscope can include imaging optics configured forreceiving signal light from a position within the sample that isilluminated by the Bessel-like beam and for imaging the received lighton a detector. The imaging optics can include a detection objectivehaving an axis oriented in a second direction that is non-parallel tothe first direction. The microscope can include beam-translation opticsconfigured for translating the position of the Bessel-like beam withinthe sample in discrete steps of more than or about λ/2NA to create afirst excitation pattern of multiple Bessel-like beams having a spatialperiod, Λ, equal to the distance between beam positions of neighboringsteps and configured to create N-1 additional excitation patterns thatare spatially phase shifted from the first excitation pattern by(N-1)Λ/N. The microscope can also include a detector configured fordetecting signal light received by the imaging optics where the detectorhas individual detection units, and can also include a processorconfigured to generate N images from the received signal light whereeach n image, for n=1 to N, is based on detected light due to excitationof the sample by the n^(th) excitation pattern and configured generate afinal image of the sample by combining the individual images accordingto

$I_{final} = {{{\sum\limits_{n = 1}^{N}{I_{n}{\exp \left( {2{{{\pi }n}/N}} \right)}}}}.}$

Implementations can include one or more of the following features. Forexample, the signal light can have a wavelength of λ/2. The signal lightcan be generated through a non-linear signal generation process. In someimplementations, N=3. The step size can be less than or about λ/NA. Insome implementations, N≧5. The step size can be greater than or aboutλ/NA. The Bessel-like beam can have a ratio of a Rayleigh length, z_(R)to a minimum beam waist, w_(o), of more than 2πw_(o)/λ and less than100πw_(o)/λ. The Bessel-like beam can have a non-zero ratio of a minimumnumerical aperture to a maximum numerical aperture of less than 0.95.The Bessel-like beam can have a non-zero ratio of a minimum numericalaperture to a maximum numerical aperture of less than 0.90. TheBessel-like beam can have a minimum numerical aperture greater than zeroand a ratio of energy in a first side of the beam to energy in thecentral lobe of the beam of less than 0.5.

The microscope an also include a coverslip that supports the samplewhere a normal direction to a plane of the sample that supports thesample forms and angle with the first direction of more than 10 degreesand less than 80 degrees. The sample can be less than ten micrometersthick. The microscope an also include an annular mask in a path of thelight beam configured to generate an annular ring of light from whichthe Bessel-like beam is formed.

In yet another general aspect, a microscope can include a light sourcefor generating a light beam having a wavelength, λ, and beam-formingoptics, including an optical element positioned in a path of the lightbeam and configured for generating an annular ring of light. Thebeam-forming optics being configured for generating from the light beaman excitation beam having a central lobe and at least one side lobe andalso configured to direct the excitation beam to a position within asample. The beam-forming optics can include an excitation objectivehaving an axis oriented in a first direction. A transverse profile ofthe excitation beam in the sample is intermediate between a profile of alowest order Bessel function and the Gaussian function. The microscopecan also include imaging optics configured for receiving signal lightfrom a position within the sample that is illuminated by the excitationbeam and for imaging the received light on a detector. The imagingoptics can include a detection objective having an axis oriented in asecond direction that is non-parallel to the first direction where thesignal light has a wavelength of λ/2. The microscope can also include adetector configured for detecting the signal light received by theimaging optics.

In another general aspect, a microscope includes a light source forgenerating a light beam having a wavelength, λ, and first beam-formingoptics configured for receiving the light beam and generating a firstBessel-like beam that is directed into a sample. The beam-forming opticsinclude a first excitation objective having a numerical aperture(NA_(EO)) and an axis oriented in a first direction. The microscopefurther includes imaging optics configured for receiving signal lightfrom a position within the sample that is illuminated by the firstBessel-like beam and for imaging the received light on a detector. Theimaging optics include a detection objective having a numerical aperture(NA_(DO)) and an axis oriented in a second direction that isnon-parallel to the first direction. The microscope includes firstbeam-translation optics configured for translating the position of thefirst Bessel-like beam within the sample in discrete steps of more thanor about λ/2NA_(EO) to create a first excitation pattern of multiplefirst Bessel-like beams having a spatial period, Λ, equal to thedistance between beam positions of neighboring steps and configured tocreate N-1 additional excitation patterns that are spatially phaseshifted from the first excitation pattern by (N-1)Λ/N. The microscopeincludes a detector having individual detection units and configured fordetecting first signal light received by the imaging optics, wherein thefirst signal light is emitted from the sample based an interaction ofthe first Bessel-like beam with the sample. The microscope includes aprocessor that is configured to generate a real space constituent imagefor each of the N excitation patterns, to Fourier transform each of thereal space constituent images to generate reciprocal space constituentimages for each of the excitation patterns, to combine the reciprocalspace constituent images to generate a final reciprocal space image, andto re-transform the final reciprocal space image to generate a finalreal space image of the sample, where the final real space image of thesample has a resolution of less that λ/2NA_(DO) in a coordinateorthogonal to the first direction.

The details of one or more implementations are set forth in theaccompanying drawings and the description below. Other features will beapparent from the description and drawings, and from the claims

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a light sheet microscopy (LSM) system.

FIG. 2 is a schematic diagram of a profile of a focused beam of light.

FIG. 3 is a schematic diagram of a Bessel beam formed by an axicon.

FIG. 4 is a schematic diagram of a Bessel beam formed by an annularapodization mask.

FIG. 5 is a schematic diagram of a system for Bessel beam light sheetmicroscopy.

FIG. 6A is a plot of the intensity profile of a Bessel beam.

FIG. 6B shows a plot of the intensity profile of a conventional beam.

FIG. 7A is a plot of the intensity profile of a Bessel beam of FIG. 6Ain the directions transverse to the propagation direction of the beam.

FIG. 7B is a plot of the intensity profile of the conventional beam ofFIG. 6B in the directions transverse to the propagation direction of thebeam.

FIG. 8A is a plot of the intensity profile in the YZ plane of a Besselbeam generated from an annular mask having a thinner annulus in theannulus used to generate the intensity profile of the Bessel beam ofFIG. 6A.

FIG. 8B is a plot of the transverse intensity profile in the XZdirections for the beam of FIG. 8A.

FIG. 9A is a schematic diagram of another system for implementing Besselbeam light sheet microscopy.

FIG. 9B is a schematic diagram of another system for implementing Besselbeam light sheet microscopy.

FIG. 10 shows a number of transverse intensity profiles for differentBessel-like beams.

FIG. 11A shows the theoretical and experimental one-dimensionalintensity profile of a Bessel-like beam at the X=0 plane.

FIG. 11B shows an integrated intensity profile when the Bessel beam ofFIG. 11A is swept in the X direction.

FIG. 12A shows plots of the width of fluorescence excitation profiles ofa swept beam, where the beam that is swept is created from annuli thathave different thicknesses.

FIG. 12B shows plots of the axial intensity profile of the beam that isswept in the Z direction.

FIG. 13A is a schematic diagram of a surface of a detector having atwo-dimensional array of individual detector elements in the X-Y plane.

FIG. 13B is a schematic diagram of “combs” of multiple Bessel-likeexcitation beams that can be created in a given Z plane, where thespacing in the X direction between different beams is greater than thewidth of the fluorescence band generated by the side lobes of theexcitation beams.

FIG. 14 shows theoretical and experimental single-harmonic structuredillumination patterns that can be created with Bessel-like beams havinga maximum numerical aperture of 0.60 and the minimum vertical apertureof 0.58, which are created with 488 nm light.

FIG. 15 shows theoretical and experimental higher-order harmonicstructured illumination patterns that can be created with Bessel-likebeams having a maximum numerical aperture of 0.60 and the minimumvertical aperture of 0.58, which are created with 488 nm light.

FIG. 16 shows a system with a galvanometer-type mirror placed at a planethat is conjugate to the detection objective between the detectionobjective and the detector.

FIG. 17A shows two overlapping structured patterns. FIG. 17B shows areciprocal space representation of one of the patterns of FIG. 17A. FIG.17C shows shows a reciprocal space representation of the other patternof FIG. 17A. FIG. 17D shows an observable region of a reciprocal spacerepresentation of specimen structure shifted from the reciprocal spaceorigin. FIG. 17E shows observable regions of reciprocal spacerepresentations of specimen structure shifted from the reciprocal spaceorigin, where the different representations correspond to differentorientations and/or phrase of a structured pattern overlayed with thespecimen structure.

DETAILED DESCRIPTION

This description discloses microscopy and imaging apparatus, systems,methods and techniques, which enable a light sheet or pencil beam tohave a length that can be decoupled from its thickness, thus allowingthe illumination of large fields of view (e.g., tens or even hundreds ofmicrons) across a plane having a thickness on the order of, or smallerthan, the depth of focus of the imaging objective by using illuminationbeams having a cross-sectional field distribution that is similar to aBessel function. Such illumination beams can be known as Bessel beams.Such beams are created by focusing light, not in a continuum ofazimuthal directions across a cone, as is customary, but rather at asingle azimuthal angle or range of azimuthal angles with respect to theaxis of the focusing element. Bessel beams can overcome the limitationsof the diffraction relationship shown in FIG. 2, because therelationship shown in FIG. 2 is only valid for lenses (cylindrical orobjectives) that are uniformly illuminated.

FIG. 3 is a schematic diagram of a Bessel beam formed by an axicon 300.The axicon 300 is a conical optical element, which, when illuminated byan incoming plane wave 302 having an approximately-Gaussian intensitydistribution in directions transverse to the beam axis, can form aBessel beam 304 in a beam that exits the axicon.

FIG. 4 is a schematic diagram of a Bessel beam 400 formed by an annularapodization mask 402, where the annular mask 402 is illuminated tocreate a thin annulus of light at the back focal plane of a conventionallens 404. The mask 402 is separated from the lens 404 by the focallength, f. An angle, θ, can be defined as the inverse tangent of halfthe distance, d, from the center of the annular ring to a point withinthe ring divided by the focal length, where d_(o) can be used to denotethe minimum diameter of the annular ring. Ideally, in either case shownby FIG. 3 or by FIG. 4, the axial wavevectors k_(z) of all raysconverging to the focus are the same, and hence there is no variation ofthe beam along this direction. In practice, the finite diameter of theaxicon 300, or the finite width, Δd, of the annular ring in theapodization mask 402 restricts the Bessel beam to a finite length. Theoptical system of the annular apodization mask 402 and the lens 404 canbe characterized by a minimum and maximum numerical aperture, where themaximum numerical aperture is proportional to d_(o)+Δd, and the minimumnumerical aperture is proportional to d_(o). In other implementations,different optical elements, other than an axicon or an apodization mask,can be used to create an annulus of light. For example, a binary phasemask or a programmable spatial light modulator can be used to create theannulus of light.

FIG. 5 is a schematic diagram of a system 500 for Bessel beam lightsheet microscopy. A light source 502 emits a light beam 504 that strikesan annular apodization mask 506. An annulus of excitation light 508illuminates the back focal plane of microscope objective 510 to createan elongated Bessel beam 512 of light in a sample 514. By scanning thisbeam in a plane 516 transverse to the axis of the Bessel beam 512 andcoincident with the focal plane of a detection objective 504 whilesimultaneously integrating the collected signal 518 with a camera 520located at a corresponding image plane of imaging optics 522, an imageis obtained from a much thinner slice within the sample than is the casewhen either conventional light sheet microscopy or DSLM is used.

How much thinner the sheet of excitation light can be with Bessel beamillumination than with conventional light sheet microscopy or DSLM canbe seen from a comparison of FIG. 6A, which shows a plot of theintensity profile of a Bessel beam, and FIG. 6B, which shows a plot ofthe intensity profile of a conventional beam. In the plots of FIGS. 5and 6, Y is along the axis of the propagation direction of the beam, Xis the direction of the excitation polarization (when linearly polarizedlight is used), and Z is along the axis of detection optics objective522 and is orthogonal to X and Y. FIG. 7A is a plot of the intensityprofile of a Bessel beam of FIG. 6A in the directions transverse to thepropagation direction of the beam, and FIG. 7B is a plot of the Gaussianintensity profile of the conventional beam of FIG. 7A in the directionstransverse to the propagation direction of the beam.

As seen in FIG. 6A, annular illumination across a small range of angles(θ=43 to 45 degrees) results in a Bessel-like beam approximately 50wavelengths λ long in the Y direction, or roughly the same lengthobtained by conventional illumination using a plane wave having aGaussian transverse intensity profile that is focused by a lens into anillumination beam having a cone half-angle of 12 degrees, as seen inFIG. 6 b. However, the thickness of the Bessel beam is much narrowerthan the thickness of the conventional beam, yielding a much thinnersheet of excitation when scanned across a plane.

Furthermore, even longer Bessel-like beams can be made withoutcompromising their cross-sectional width simply by restricting theannular illumination over an even smaller range of angles. FIG. 8A is aplot of intensity profile in the YZ directions of a Bessel beamgenerated from an annular mask having a thinner annulus that is used togenerate the intensity profile of the Bessel-like beam of FIG. 6A, andFIG. 8B is a plot of the transverse intensity profile for the beam inthe XZ directions. As shown in FIG. 8A, annular illumination across asmall range of angles (θ=44 to 45 degrees) results in in the YZintensity profile of the Bessel-like beam shown in FIG. 8A, where theBessel-like beam has a length of approximately 100 wavelengths in the Ydirection. However, the transverse intensity profile of the longerBessel beam is relatively unchanged compared with shorter Bessel beam,as can be seen from a comparison of FIG. 7A and FIG. 8B, and thethickness of the beam is not significantly greater than the thickness ofthe beam whose intensity profile is shown in FIG. 6A. In contrast, withconventional illumination the usual approach of lengthening the beam byreducing the NA results in an unavoidably larger diffraction limitedcross-section, roughly in accordance with Table 1.

FIG. 9A is a schematic diagram of another system 900 for implementingBessel beam light sheet microscopy. Collimated light 901, such as alaser beam having a Gaussian intensity profile, is reflected from firstgalvanometer-type mirror 902 and then imaged by relay lens pair 903 and904 onto a second galvanometer-type mirror 905 positioned at a pointoptically conjugate to the first galvanometer-type mirror 902. A secondlens pair 906 and 907 then relays the light to annular apodization mask908 conjugate with the second galvanometer-type mirror 905. The annularlight beam transmitted through this mask 908 is then relayed by a thirdlens pair 910 and 911 onto a conjugate plane coincident with the backfocal plane of excitation objective 912. Finally, the annular light isfocused by objective 912 to form a Bessel-like beam 913 that is usedprovides excitation light to a specimen.

The rotational axis of galvanometer mirror 902 is positioned such thattilting this galvanometer-type mirror 902 causes the Bessel-like beam913 to sweep across the focal plane of detection objective 915 (i.e., inthe X direction), whose axis is orthogonal to (or whose axis hasn'torthogonal complement to) the axis of the excitation objective 912. Thesignal light 914 can be directed by detection optics, including thedetection objective 915, to a detection camera 917. Thegalvanometers-type mirrors 902, 905 can provide sweep rates of up toabout 2 kHz, and with resonant galvanometer-type mirrors (e.g.,Electro-Optical Products Corp, model SC-30) sweep rates can exceed 30kHz. Extremely high frame rate imaging is then possible when the systemis used in conjunction with a high frame rate detection camera (e.g.,500 frames/sec with an Andor iXon+ DU-860 EMCCD, or >20,000 frames/secwith a Photron Fastcam SA-1 CMOS camera coupled to a Hamamatsu C10880-03image intensifier/image booster).

The rotational axis of the galvanometer mirror 905 is positioned suchthat tilting of this mirror causes Bessel-like beam 913 to translatealong the axis of detection objective 915. By doing so, different planeswithin a specimen can be accessed by the Bessel beam, and a threedimensional (3D) image of the specimen can be constructed, with muchhigher axial resolution than in conventional light sheet microscopy, dueto the much narrower sheet of excitation afforded by Bessel-likeexcitation. In order to image each plane in focus, either detectionobjective 915 must be moved synchronously with the motion of the Besselbeam 913 imparted by the tilt of galvanometer-type mirror 905 (such aswith a piezoelectric transducer (e.g., Physik Instrumente P-726)), orelse the effective plane of focus of the detection objective 915 must bealtered, such as by using a second objective to create a perfect imageof the sample. Of course, if 3D image stacks are not desired, the secondgalvanometer 905 and relay lenses 906 and 907 can be removed from thesystem shown in FIG. 9A, and the first galvanometer 902 and relay lenses903 and 904 can be repositioned so that the apodization mask 908 is at aconjugate plane relative to galvanometer-type mirror 902. Anacousto-optical tunable filter (AOTF) 918 can be used to block allexcitation light from reaching the specimen when desired.

The system in FIG. 9A is typically quite wasteful of the energy in lightbeam 901, because most of this light is blocked by apodization mask 908.If greater efficiency is desired, a diffractive optical element such asa binary phase mask or spatial light modulator and a collimating lenscan be used to create an approximately annular light beam prior to moreexact definition of this beam and removal of higher diffractive ordersby the apodization mask 908.

In another implementation, shown in FIG. 9B, signal eight 914 receivedby detection objective 915 can be transmitted through relay lenses 920,922 and reflected off a galvanometer-type mirror 924 and thentransmitted through relay lenses 926 and 928 and focused by a tube lens930 onto a detector 932. An aperture mask (e.g., an adjustable slit) 934can be placed at a focal plane of lens 926, and the when the maskdefines a slit the width of the slit 934 can be selected to block signallight from positions in the sample corresponding to side lobes of theBessel-like beam illumination light, while passing signal light frompositions in the sample corresponding to the central peak of theBessel-like beam illumination light. The galvanometer-type mirror 924can be rotated in conjunction with galvanometer-type mirror 902, so thatwhen the Bessel-like beam is scanned in the X direction within thesample signal light from different positions within the sample passesthrough the slit 934.

Bessel-like beams include excitation intensity in rings other than thecentral excitation maximum, which as are evident in FIGS. 7A and 8B, andsubstantial energy resides in the side lobes of a Bessel-like beam.Indeed, for an ideal Bessel beam of infinite extent, each side lobecontains energy equal to that in the central peak. Also, for an idealBessel beam the ratio of the Rayleigh length of the beam to the minimumwaist size of the beam is infinite. FIG. 10 shows a number of transverseintensity profiles for different Bessel-like beams. In FIG. 10, thefirst column shows theoretical two-dimensional intensity plots in the XZplane, the second column shows experimental intensity plots in the thirdcolumn shows a one-dimensional intensity profile at the X=0 plane.Different rows in FIG. 10 correspond to Bessel-like beams that arecreated using different annular apodization masks. Each row indicatesthe maximum and minimum numerical aperture of the annular ring of themask. In the first row, the maximum numerical aperture is 0.80, and theminimum numerical aperture is 0.76. In the second row, the maximumnumerical aperture is 0.60, and the minimum numerical aperture is 0.58.In a third row, the maximum numerical aperture is 0.53 and the minimumnumerical aperture is 0.51. In the fourth row the maximum numericalaperture is 0.40, and the minimum numerical aperture is 0.38. In thefifth row, the maximum numerical aperture is 0.20, and the minimumnumerical aperture is 0.18.

Because of the intensity in the side lobes, the integrated fluorescenceexcitation profile after the beam is swept in the X direction exhibitsbroad tails, as shown in FIG. 11. FIG. 11A shows the theoretical andexperimental intensity profile in the Z direction of a Bessel-like beam,when the center of the beam is fixed at the X=0 and Z=0 plane, whereexperimental values are shown by dots and theoretical values are shownby solid lines. The intensity profile shown in FIG. 11A isrepresentative of a Bessel-like beam formed from an annular apodizationmask that generates an annulus of 488 nm light at a rear pupil of anexcitation objective, where the annulus has a maximum numerical apertureof 0.60 and a minimum numerical aperture of 0.58. When this Bessel-likebeam is swept in the X direction to create a sheet of excitation lightcentered on the Z=0 plane, integrated fluorescence excitation profileshown in FIG. 11B results because of the side lobes in the beam. Thus,the side lobes of the Bessel beam can contribute out-of-focus backgroundfluorescence and premature photobleaching of the sample. A number oftechniques can be used to mitigate the effect of these lobes.

Choosing a thicker annulus in the annular mask 506 suppresses thesetails, but it does so at the expense of the length of the beam, as thebeam becomes more Gaussian and less Bessel-like in character. Thiseffect can be seen in FIG. 12A and FIG. 12B. FIG. 12A shows plots of thewidth of fluorescence excitation profiles of beams swept in the Xdirection in the Z=0 plane, where the beams that are swept are createdfrom annuli that have different thicknesses. FIG. 12B shows plots of theaxial intensity profiles (i.e., in the Y direction) of the beams thatare swept. For each of the beams whose intensity profiles are plotted inFIG. 12A and FIG. 12B, the maximum numerical aperture is 0.60. A beamwith an intensity profile 1202 has a minimum numerical aperture equal to0.58. A beam with an intensity profile 1204 has a minimum numericalaperture equal to 0.56. A beam with an intensity profile 1206 has aminimum numerical aperture people equal to 0.52. The beam with anintensity profile 1208 has a minimum numerical aperture equal to 0.45. Abeam with an intensity profile 1210 has a minimum numerical apertureequal to 0.30. A beam with an intensity profile 1212 as a minimumnumerical aperture equal to 0.00, i.e., it is equivalent to the Gaussianbeam that fully illuminates a circular aperture.

Thus, as can be seen from a comparison of the plot FIG. 12A and FIG.12B, a trade-off exists between minimizing the deleterious effects ofthe side lobes of the beam and maximizing the axial length of the fieldof view of the beam. Therefore, by selecting an annulus having athickness that achieves a length of the field of view that is justsufficient to to cover a region of interest in a specimen, but that isnot substantially longer than the region of interest, the deleteriouseffects of the side lobes can be minimized. Therefore, the system 500shown in FIG. 5, can include a plurality of different apodization masks506 in which the thickness of the open annular region various, and aparticular one of the apodization masks 506 can be selected to image aregion of the specimen 514, where the selected mask is chosen such thatthe length of the field of view of beam just covers the region ofinterest. When referring to FIG. 4, the different apodization masks canhave open regions with different widths, Δd.

Thus, a comparison of the plots in FIG. 12A and FIG. 12B shows theprofiles of the beam changing from a profile that best approximates thatof a lowest order (J₀) Bessel function (plot 1202) to a Gaussian profile(1212). This comparison indicates that the deleterious effect of theside lobes can be reduced by using a beam having a profile that is notsubstantially similar to that of a Bessel function, at the expense ofhaving a beam with a shorter axial length. This means that it can beadvantageous to select a beam profile having a minimum length necessaryto create the desired image, so that the effect of the side lobes of thebeam, which create background haze and photobleaching, can be minimized.Thus, the beam that may be selected may not have a profile thatapproximates that of a Bessel function, but the beam also may not have aprofile of a Gaussian beam, because the annular mask 506 blocks theportion of the incoming light 504 on the axis of the excitationobjective 510 such that the k_(z)=0 of the beam 516 are removed. Inparticular, in one implementation the selected beam can have a ratio ofa Rayleigh length, z_(R) to a minimum beam waist, w_(o), of more than2πw_(o)/λ and less than 100πw_(o)/λ. In another implementation, theselected beam can have a non-zero ratio of a minimum numerical apertureto a maximum numerical aperture of less than 0.95. In anotherimplementation, the selected beam can have a non-zero ratio of a minimumnumerical aperture to a maximum numerical aperture of less than 0.9. Inanother implementation, the selected beam can have a ratio of a minimumnumerical aperture to a maximum numerical aperture of less than 0.95 andgreater than 0.80. In another implementation, the selected beam can havea non-zero ratio of a minimum numerical aperture to a maximum numericalaperture of less than 0.9. In another implementation, the selected beamcan have a ratio of a minimum numerical aperture to a maximum numericalaperture of less than 0.95 and greater than 0.80. In anotherimplementation, the selected beam can have a ratio of energy in a firstside lobe of the beam to energy in the central lobe of the beam of lessthan 0.5.

The length of the beam 516, which is necessary to image a specimen canbe reduced by tilting a cover slip that supports the specimen withrespect to the direction of the incoming beam 516. For example, if aspecimen that resides on a cover slip is 5 μm thick in the directionnormal to the cover slip and has lateral dimensions of 50 μm×50 μm then,if the cover slip lies in the Z=0 plane, the beam 516 would have to be50 μm long to span the specimen. However, by tilting the plane of thecover slip at a 45° angle to the direction of the incoming beam 516,then the beam would only need to be 5 μm>√2 long to span the sample.Thus, by placing a thin specimen on a cover slip and tilting the coverslip with respect to the direction of the incoming beam, a shorterlength beam can be used, which has the advantage of reducing the effectof background haze and photobleaching due to side lobes of the beam. Toimage the specimen on a tilted cover slip, the beam 516 can be scannedin the X direction by tilting the galvanometer-type mirror 902, and canbe scanned in the Z direction either by introducing a third galvanometer(not shown) and a third pair of relay lenses (not shown) into the system900 shown in FIG. 9A to scan the beam 516 in the Z direction or bytranslating the Z position of the specimen, e.g., via a piezoelectrictransducer (not shown and FIG. 9A) coupled to the cover slide thatsupports the specimen. This mode of operation in which a specimen on acover slip is imaged when the cover slip is tilted (e.g., at an anglebetween 10 and 80 degrees) with respect to the direction of the incomingillumination beam can be used to image thin (e.g., less than 10 μmthick) specimens, such as individual cells that are mounted or culturedon to the cover slip.

Another approach to isolate the central peak fluorescence from thatgenerated in the side lobes is to exclude the latter via confocalfiltering with a virtual slit. When the detector includes a plurality ofindividual detector elements, only those elements of the detector uponwhich an image the portion of the sample that is illuminated by thecentral lobe of the illumination beam can be activated to recordinformation that is used to generate an image, while the individualdetector elements upon which an image of the portion of the sample thatis illuminated by side lobes of the illumination beam are not activated,such that they do not record information that is used to generate animage.

For example, FIG. 13A is a schematic diagram of a surface of a detectorhaving a two-dimensional array of individual detector elements in the XYplane. When the center of the central lobe of the excitation beam islocated at X=0 and side lobes are located at X>0 and X<0, then thedetector elements 1302 onto which fluorescence or detection light isfocused from the X=0 position within the specimen at the focal plane ofthe detection objective 915 (or detector elements corresponding to thesmallest absolute value of X for a particular Y position) can beactivated to record information, while neighboring detector elementscorresponding to higher absolute values of X for the particular Yposition can be un-activated such that they do not record informationthat is used to generate an image. As shown in FIG. 13A, detectorelements 1302 located on the detector surface at positions thatcorrespond most closely with fluorescence light from X=0 positionswithin the specimen can be activated to record information, whileneighboring detector elements 1304, 1306 are unactivated, so they do notrecord fluorescence light from positions within the sample that are notilluminated by the central portion of the excitation beam.

FIG. 13B is a schematic diagram of “combs” of multiple Bessel-likeexcitation beams that can be created in a given Z plane. A comb of beamscan be created by inserting a diffractive optical element (DOE, notshown) in the beam path between the light source and thegalvanometer-type mirrors 902, 905, where the DOE diffracts a pluralityof beams at different angles from the DOE, which end up being parallelto and spatially shifted from each other within the specimen. In thespecimen at the focal plane of the detection objective, the spacing inthe X direction between different beams of the comb is greater than thewidth of the fluorescence band generated by the side lobes of the beams.This allows information to be recorded simultaneously from rows ofindividual detector elements corresponding to the centers of thedifferent beams of the comb, without the side lobes of neighboring beamsinterfering with the recorded signal for a particular beam.

For example, as shown in FIG. 13B, a comb of beams that illuminate aplane of a specimen 1308 can include the beams A1, B1, C1, D1, and E1,where the beams are separated by distances great enough so that sidelobes of one beam in the comb do not overlap with a central portion of aneighboring beam. In this manner, multiple “stripes” of an image can besimultaneously recorded. This process is then repeated, with additionalimages collected as the comb of Bessel-like illumination beams istranslated in discrete steps having a width that corresponds to thespacing in the X direction between individual detector elements untilall “stripes” of the final image have been recorded. For example, thebeams can be moved to new positions of A2, B2, C2, D2, and E2, where thespacing between the positions A1 and A2, the spacing between positionsB1 and B2, etc. corresponds to the spacing between neighboringindividual detector elements in the detector. Thus, fluorescence lightfrom the beam position C1 could be detected at a detector element 1302,while fluorescence light from the beam position C2 can be detected atindividual detector elements 1304. The image is that then digitallyconstructed from the information in all of the different stripes of theimage. An acousto-optical tunable filter (AOTF) 918 can be used to blockall excitation light from reaching the specimen between steps.

Another technique to reduce the influence of the side lobes and toimprove the point reduce the Z-axis size of the field of view from whichdetection light is received to employ structured illumination (SI) basedoptical sectioning. In a widefield λ, microscopy implementation of SI, aperiodic excitation pattern is projected through an epi-illuminationobjective to the focal plane of the objective, and three images of asample, I_(n) (n=1,2,3), are acquired as the pattern is translated insteps of ⅓ of the period of the pattern. Since the observable amplitudeof the pattern decreases as it becomes increasingly out of focus (i.e.,in a direction perpendicular to the focal plane), combining the imagesaccording to:

$\begin{matrix}{I_{final} = {{\sum\limits_{n = 1}^{N}{I_{n}{\exp \left( {2{{{\pi }n}/N}} \right)}}}}} & (1)\end{matrix}$

with N=3 removes the weakly modulated out-of-focus component and retainsthe strongly modulated information near the focal plane. In equation(1), I is an intensity at a point in the image, and n is an index valueindicating an image from which I_(n) is taken. Equation (1) is by oneexample of a linear combination of the individual images that willremove the weakly modulated out-of-focus component and retain thestrongly modulated information near the focal plane.

To use SI using a Bessel-like beam with a wavelength, λ, thatilluminates a thin plane of a specimen and where light is emitted in adirection perpendicular to (or in a direction with a componentperpendicular to) the illumination plane, the beam is not sweptcontinuously, but rather is moved in discrete steps to create a patternof illumination light from which an image I_(n) can be generated. Whenthe stepping period is larger than or approximately equal to the minimumperiod of λ/2NA_(Bessel) ^(max) required to produce a resolvablegrating, but smaller than or approximately equal to λ/NA_(Bessel)^(max), the imposed pattern of illumination light contains a singleharmonic, as required for the three-image, three-phase SI algorithm.

Thus, referring to FIG. 9A, the Bessel-like beam 913 can be swept in theX direction in discrete steps having a period greater than orapproximately equal to λ/2NA_(Bessel) ^(max) and less than orapproximately equal to λ/NA_(Bessel) ^(max) by controlling the positionof the galvanometer-type mirror 902, and detection light can be receivedand signals corresponding to the detected light can be recorded by thedetector 917 when the beam 913 is in each of the positions. While thegalvanometer-type mirror is being moved from one position to the nextposition the illumination light can be blocked from reaching the sampleby the AOTF. In this manner, an image I₁ can be generated from thedetected light that is received when the illumination beam 913 is ateach of its staff positions. Then, additional images, I₂ . . . I_(N),can be created by again stepping the beam 913 across the specimen in theX direction to create a pattern of illumination light, but with thepatterns spatially shifted from the position of the first pattern by(i-1)/N of the period of the pattern, for i=2 to N. A final image of thespecimen then can be constructed from the recorded signals through theuse of equation (1).

FIG. 14 shows a theoretical and experimental structured illuminationpatterns that can be created with a Bessel-like beams having a maximumnumerical aperture of 0.60 and the minimum vertical aperture of 0.58,which are created with 488 nm light. The leftmost column of figuresshows theoretical patterns, the middle column showsexperimentally-measured patterns, and the third column showsone-dimensional intensity patterns for the Z=0 plane (top figure) andthe X=0 (bottom figure) plane. In the first row of FIG. 14, the periodthe pattern (i.e., the spacing between successive positions of thecenter of the Bessel-like being is the beam is stepped in the Xdirection) is 0.45 μm. In the second row, the period of the pattern is0.60 μm. In the third row the period of the pattern is 0.80 μm. Asdescribed above, a comb of multiple Bessel-like beams, which are spacedby more than the width of the fringes of the beams in the comb, can beused to illuminate the specimen simultaneously, and then the comb ofbeams can be stepped in the X direction using the step size describedabove, so that different stripes of the specimen can be imaged inparallel and then an image of the specimen can be constructed from themultiple stripes.

The excellent optical sectioning of the single harmonic SI mode resultsfrom the removal of the k_(x)=0 band in the excitation modulationtransfer function (MTF) under application of Eq. (1). However, due tothe energy in the Bessel side lobes, considerably more spectral energyexists in this band than in the two side bands, so that its removalproves wasteful of the photon budget and reduces the SNR of the finalimages substantially. Somewhat more energy can be transferred to theside bands using single harmonic excitation having a period far beyondthe λ/2NA_(detect) ^(max) Abbe limit, but at the expense ofproportionally poorer optical sectioning capability.

An alternative that can better retain both signal and axial resolutionis to create a multi-harmonic excitation pattern by stepping the beam ata fundamental period larger than λ/NA_(Bessel) ^(max), as seen in FIG.15, which shows theoretical and experimental higher-order harmonicstructured illumination patterns that can be created with Bessel-likebeams having a maximum numerical aperture of 0.60 and the minimumvertical aperture of 0.58, which are created with 488 nm light. Tocreate a single SI image with a pattern having H harmonics, Eq. (1) isagain used, except with N≧H+2 images, each with the pattern phaseshifted by 2π/N relative to its neighbors. With increasing H, more sidebands are generated in the MTF that contain a greater combined fractionof the total spectral energy relative to the k_(x)=0 band, thus yieldinghigher signal-to-noise (SNR) images. Due to the greater weighting ofthese sidebands to lower k_(z), axial resolution (i.e., along the axisof the detection objective 915) of this multi-harmonic SI mode isslightly less (0.29 μm FWHM for N=9 phases) than in the single harmoniccase, yet images of fixed and living cells still exhibit isotropic 3Dresolution, albeit at the cost of more data frames required per imageplane, and thus lower speed.

In addition to this speed penalty, both single-harmonic andmulti-harmonic SI modes still generate some excitation beyond the focalplane, and are thus not optimally efficient in their use of the photonbudget. Both these issues can be addressed using two-photon excitation(TPE), which suppresses the Bessel side lobes sufficiently such that athin light sheet can be obtained even with a continuously swept beam. Asa result, high axial resolution and minimal out-of-focus excitation isachieved in fixed and living cells with only a single image per plane.Some additional improvement is also possible with TPE-SI, but the fasterTPE sheet mode can be preferred for live cell imaging. The benefits ofTPE are not limited to structured illumination excitation of thespecimen, but are beneficial during other modes of Bessel-like beamplane illumination of the specimen to reduce out of focus excitation andphoto damage by the illumination beam. Other forms of non-linearexcitation with a Bessel like beam, such as coherent anti-Stokes Ramanscattering (CARS), can also reap similar benefits.

Thus, the improved confinement of the excitation light to the vicinityof the focal plane of the detection objective made possible by Besselbeam plane illumination leads to improved resolution in the axialdirection (i.e., in the direction along the axis of the detectionobjective) and reduced photobleaching and phototoxicity, therebyenabling extended observations of living cells with isotropic resolutionat high volumetric frame rates. For example, extended imaging of theendoplasmic reticulum in a live human osteosarcoma cell (U2OS cell line)in the linear multi-harmonic SI mode was performed. Despite the factthat over three-hundred image slices were required to construct each 3Dimage stack, the dynamics of the ER could be followed over 45 minutes ata rate of 1 stack/min with axial resolution of ˜0.3 μm.

Even longer duration observations were found to be possible in the TPEsheet mode. For example, portions of three consecutive image stacks froma series of one hundred such stacks showed the evolution of numerousfilopodia on the apical surface of a HeLa cell transfected withmEmerald/Lifeact. Significantly, the imaging speeds achievable in thismode (51.4 image planes/sec, 6 sec stack interval) enable even complex,rapid 3D cellular processes to be visualized with sufficient timeresolution. This is further underscored by consecutive images of theretrograde flow of membrane ruffles formed at the leading edge of atransformed African green monkey kidney cell (COS-7 cell line,transfected with mEmerald/c-src). Such ruffles can surround and engulfextracellular fluid to create large intracellular vacuoles, a processknown as macropinocytosis, which was directly demonstrated using thetechniques described herein. The visualization of these processes infour dimensional spatiotemporal detail (0.12×0.12×0.15 μm×12.3 sec stackinterval) across 15 minutes cannot currently be achieved with otherfluorescence microscopy techniques.

For sufficiently bright samples, the pixel rate of EMCCD cameras becomesa limiting factor. To achieve even higher imaging speeds in such cases,a scientific CMOS camera (125 MHz, Hamamatsu Orca Flash 2.8) can beused. To exploit the full speed of the camera, a third galvanometer-typemirror that can be tilted can be placed at a plane conjugate to the rearpupil of the detection objective and used to tile several image planesacross the width of the detector, which were then are read out inparallel.

FIG. 16 shows a system 1600 with a mirror placed at a plane that isconjugate to the detection objective between the detection objective andthe detector. In the system 1600, detection light collected by detectionobjective 1602 can be focused by a tube lens 1604 to form an image atthe plane of an adjustable slit 1606. The image cropped by theadjustable slit 1606 is reimaged by relay lenses 1608 onto a high-speeddetection camera 1610. A galvanometer-type mirror 1612 is placed theplane between the relay lenses 1608 that is conjugate to the back focalplane of the detection objective 1612. By changing the angle ofgalvanometer-type mirror, multiple images can be exposed across thesurface of the detection camera 1610 and then read out in parallel toexploit the full speed of the detection camera 1610.

With this configuration, the 3D dynamics of chromatid separation inearly anaphase could be studied in the TPE sheet mode at rates of 1volume/sec. Significantly, even at these imaging rates, the excitationdid not arrest mitosis. Moreover, the intracellular trafficking ofvesicles in a COS-7 cell could be observed over the course of 7000frames acquired in a single plane at 191 frames/sec.

Three-dimensional live cell imaging can be performed with Bessel-likebeans with the use of fluorescent proteins to highlight selectedportions of a specimen. A key aspect of fluorescent proteins (FPs) isthat their spectral diversity permits investigation of the dynamicinteractions between multiple proteins in the same living cell. Forexample, after transfection with mEmerald/MAP4 and tdTomato/H2B,microtubules in a pair of U2OS cells surrounding their respectivenuclei, were imaged in the linear, nine-phase multi-harmonic SI mode.Nevertheless, although many vectors are available for linear imaging,the need for N frames of different phase per image plane can limits theuse of SI with Bessel-like beams to processes which evolve on a scalethat matches the time required to collect frames at the desired spatialresolution. Of course, this limitation does not apply for fixed cells,where the linear SI mode is preferred, due to its superior axialresolution and the availability of a wider array of fluorescent dyes aswell as FPs for protein specific labeling. For example, three-colorisotropic 3D imaging of the actin cytoskeleton of an LLC-PK1 cellstained with Alexa Fluor 568 phalloidin, the nuclear envelope taggedwith mEmerald/lamin B1, and nuclear histones tagged with mNeptune/H2Bwas performed.

For imaging multiple proteins exhibiting faster dynamics, the TPE sheetmode can be used. However, this presents its own challenges: orange/redFPs such as tdTomato and mCherry do not have the same TPE brightness andphotostability of green FPs such as EGFP or mEmerald and require asecond expensive ultrafast light source, since the time required toretune and realign a single source is prohibitive for live cell imaging.Fortunately, the 3D isotropic resolution of the Bessel TPE sheet modepermits multiple proteins tagged with the same FP to be imagedsimultaneously, as long as they are known a priori to be spatiallysegregated. For example, the fragmentation of the Golgi apparatusbetween metaphase (t=0 min) and anaphase (t=10 min) was observed, asidentified by chromosome morphology (green), and the re-constitution ofthe Golgi (t=20 min) around the daughter nuclei in telophase (t=40 min)

As described herein, Bessel beam plane illumination microscopytechniques offer 3D isotropic resolution down to ˜0.3 μm, imaging speedsof nearly 200 planes/sec, and the ability, in TPE mode, to acquirehundreds of 3D data volumes from single living cells encompassing tensof thousands of image frames. Nevertheless, additional improvements arepossible. First, substantially greater light collection making stillbetter use of the photon budget would be obtained by using a detectionobjective with a numerical aperture of 1.0 or greater. Althoughmechanical constraints would thereby force the use of an excitationobjective with a numerical aperture of less than 0.8 thus lead to asomewhat anisotropic point spread function (PSF), the volumetricresolution would remain similar, since the slight loss of axialresolution would be offset by the corresponding transverse gain.

As noted above, SI using the algorithm in Eq. (1) is also photoninefficient, as it achieves high axial resolution by removingsubstantial spectral energy that resides in the k_(x)=0 band of the MTF.An alternative would be to use the algorithms of 3D superresolution SI,which assign the sample spatial frequencies down-modulated by all bandsof the excitation to their appropriate positions in an expandedfrequency space. By doing so, shorter exposure times and fewer phasesmay be needed to record images of acceptable SNR, making linear BesselSI a more viable option for high speed multicolor imaging. In addition,resolution could be extended to the sum of the excitation and detectionMTF supports in each direction—an argument in favor of using threemutually orthogonal objectives. Indeed, the marriage of Bessel beamplane illumination and 3D superresolution SI may permit the latter to beapplied to thicker, more densely fluorescent specimens than theconventional widefield approach, while more efficiently using the photonbudget.

Superresolution SI can be performed by extending the structuredillumination techniques described above with respect to FIG. 14 and FIG.15. By illuminating the sample with a structured illumination patternnormally inaccessible high-resolution information. An image of a samplecan be made accessible in the form of moire fringes. A series of suchimages can be processed to extract this high-frequency information andto generate reconstruction of the image with improved resolutioncompared to the diffraction limited resolution.

The concept of super resolution SI exploits the fact that when twopatterns are superimposed multiplicatively a beat pattern will appear inthe product of the two images, as seen in FIG. 17A. In the case ofBessel-like beam plane illumination microscopy, one of the patterns canbe the unknown sample structure, for example, the unknown spatialdistribution of regions of the sample that receive illumination lightand that emit signal light—and the other pattern can be the purposelystructured pattern of excitation light that is written in the form ofparallel Bessel-like beams. Because the amount of signal light emittedfrom a point in the sample is proportional to the product of the localexcitation light intensity and the relevant structure of the sample, theobserved signal light image that is detected by the detector will showthe beat pattern of the overlap of the two underlying patterns. Becausethe beat pattern can be coarser than those of the underlying patterns,then because the illumination pattern of the Bessel-like beams is known,the information in the beat pattern can be used to determine thenormally unresolvable high-resolution information about the sample.

The patterns shown in FIG. 17A can be Fourier transformed intoreciprocal space. For example, the Fourier transform of the structure ofa sample that is imaged by an optical system is constrained by the Abberesolution limit would be represented by a circle having a radius of2NA/λ, as shown in FIG. 17B, where the low resolution components of thesample are close to the origin, and the high-resolution components areclose to the edge of the circle. The Fourier transform of a 2Dillumination pattern that consists of a sinusoidal variation in theillumination light in one dimension area having a period equal to thediffraction limit of the optical system has only three non-zero pointsthat lie on the circle of FIG. 17B, as shown in FIG. 17C. One pointresides at the origin and the other two points are offset from theorigin in a direction defined by the orientation of the illuminationpattern by distance a proportional to the inverse of the spatial periodof the pattern. When the specimen is illuminated by structuredillumination, the resulting beat pattern between the specimen structureand the illumination structure represents information that has changedposition in reciprocal space, such that the observable region of thesample in physical space then contains new high-frequency informationrepresented by the two regions and FIG. 17D that are offset from theorigin.

In an implementation using a structured illumination pattern ofBessel-like beams, as explained above with respect to FIG. 14 and FIG.15, three images can be recorded with the spatial phase of theillumination pattern shifted by 120° between each image in both the Xdirection and in the Z direction. Then, a Fourier transform can beperformed on each of the three images, and the reciprocal space imagesare moved to their true positions in reciprocal space, combined througha weighted-average in reciprocal space, and then the weight-averagedreciprocal space image can be re-transformed to real space to provide animage of the sample. In this manner, a superresolution image of thesample can be obtained, where the resolution of the image in both the Xand Z directions can be enhanced by a factor of two over the Abbediffraction limited resolution.

In another implementation, more than one excitation objective can beused to provide a structured illumination pattern to the sample, wherethe different excitation objectives can be oriented in differentdirections, so that super resolution of the sample can be obtained inthe directions transverse to the Bessel-like beams of each of theorientation patterns. For example, a first excitation objective can beoriented with its axis along the Y direction (as described above) andcan illuminate the sample with an illumination pattern of Bessel-likebeams that provides a superresolution image of the sample in the X and Zdirections, and a second excitation objective can be oriented with itsaxis along the X direction and can illuminate the sample with anillumination pattern of Bessel-like beams that provides asuperresolution image of the sample in the Y and Z directions. Thesuperresolution information that can be derived from illuminationpatterns from the different excitation objectives

In another implementation, highly inclined, objective-coupled sheetillumination has been used to image single molecules in thicker regionsof the cell where autofluorescence and out-of-focus excitation would beotherwise prohibitive under widefield illumination. With the thinnerlight sheets possible with Bessel beam plane illumination, only in-focusmolecules would be excited, while out-of-focus ones would not beprematurely bleached. As such, it would be well suited to live cell 3Dparticle tracking and fixed cell photoactivated localization microscopy.

At the other extreme, the TPE sheet mode may be equally well suited tothe imaging of large, multicellular specimens, since it combines theself-reconstructing property of Bessel beams with the improved depthpenetration in scattering media characteristic of TPE. In addition tolarge scale 3D anatomical mapping with isotropic resolution, at highframe rates it might be fruitfully applied to the in vivo imaging ofactivity in populations of neurons.

Implementations of the various techniques described herein may beimplemented in digital electronic circuitry, or in computer hardware,firmware, software, or in combinations of them. Implementations mayimplemented as a computer program product, i.e., a computer programtangibly embodied in an information carrier, e.g., in a machine-readablestorage device or in a propagated signal, for execution by, or tocontrol the operation of, data processing apparatus, e.g., aprogrammable processor, a computer, or multiple computers. A computerprogram, such as the computer program(s) described above, can be writtenin any form of programming language, including compiled or interpretedlanguages, and can be deployed in any form, including as a stand-aloneprogram or as a module, component, subroutine, or other unit suitablefor use in a computing environment. A computer program can be deployedto be executed on one computer or on multiple computers at one site ordistributed across multiple sites and interconnected by a communicationnetwork.

Method steps may be performed by one or more programmable processorsexecuting a computer program to perform functions by operating on inputdata and generating output. Method steps also may be performed by, andan apparatus may be implemented as, special purpose logic circuitry,e.g., an FPGA (field programmable gate array) or an ASIC(application-specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read-only memory ora random access memory or both. Elements of a computer may include atleast one processor for executing instructions and one or more memorydevices for storing instructions and data. Generally, a computer alsomay include, or be operatively coupled to receive data from or transferdata to, or both, one or more mass storage devices for storing data,e.g., magnetic, magneto-optical disks, or optical disks. Informationcarriers suitable for embodying computer program instructions and datainclude all forms of non-volatile memory, including by way of examplesemiconductor memory devices, e.g., EPROM, EEPROM, and flash memorydevices; magnetic disks, e.g., internal hard disks or removable disks;magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor andthe memory may be supplemented by, or incorporated in special purposelogic circuitry.

To provide for interaction with a user, implementations may beimplemented on a computer having a display device, e.g., a cathode raytube (CRT) or liquid crystal display (LCD) monitor, for displayinginformation to the user and a keyboard and a pointing device, e.g., amouse or a trackball, by which the user can provide input to thecomputer. Other kinds of devices can be used to provide for interactionwith a user as well; for example, feedback provided to the user can beany form of sensory feedback, e.g., visual feedback, auditory feedback,or tactile feedback; and input from the user can be received in anyform, including acoustic, speech, or tactile input.

While certain features of the described implementations have beenillustrated as described herein, many modifications, substitutions,changes and equivalents will now occur to those skilled in the art. Itis, therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the true spiritof the implementations.

1. A microscope comprising: a light source for generating a light beamhaving a wavelength, λ; beam-forming optics configured for receiving thelight beam and generating a Bessel-like excitation beam that is directedinto a sample, the beam-forming optics including an excitation objectivehaving an axis oriented in a first direction; imaging optics configuredfor receiving signal light from a position within the sample that isilluminated by the Bessel-like beam and for imaging the received signallight on a detector, the imaging optics including a detection objectivehaving an axis oriented in a second direction that is non-parallel tothe first direction; a detector configured for detecting signal lightreceived by the imaging optics; and an aperture mask positioned betweenthe sample and the detector configured to prevent light illuminated byside lobes of the Bessel beam from reaching the detector, while allowinglight illuminated by a central lobe of the Bessel beam to reach thedetector.
 2. The microscope of claim 1, further comprising beam scanningoptics configured for scanning the Bessel-like beam in a directionhaving a component perpendicular to the first direction.
 3. Themicroscope of claim 2, further comprising image-positioning opticspositioned in an optical path between the sample and the detector andconfigured for imaging signal light from different positions with thesample while the Bessel-like beam is scanned by the beam scanning opticsthrough a fixed position of the aperture mask.
 4. The microscope ofclaim 3, wherein the aperture mask defines a slit.
 5. The microscope ofclaim 3, wherein the detector is a line detector.
 6. The microscope ofclaim 1, wherein the Bessel-like beam has a ratio of a Rayleigh length,z_(R) to a minimum beam waist, w_(o), of more than 2πw_(o)/λ and lessthan 100πw_(o)/λ.
 7. The microscope of claim 1, wherein the Bessel-likebeam has a non-zero ratio of a minimum numerical aperture to a maximumnumerical aperture of less than 0.95.
 8. The microscope of claim 1,wherein the Bessel-like beam has a non-zero ratio of a minimum numericalaperture to a maximum numerical aperture of less than 0.90.
 9. Themicroscope of claim 1, wherein the Bessel-like beam has a minimumnumerical aperture greater than zero and a ratio of energy in a firstside lobe of the beam to energy in the central lobe of the beam of lessthan 0.5.
 10. The microscope of claim 1, further comprising a coverslipthat supports the sample, wherein a normal direction to a plane of thesample that supports the sample forms an angle with the first directionof more than 10 degrees and less than 80 degrees.
 11. The microscope ofclaim 10, wherein the sample is less than ten micrometers thick.
 12. Themicroscope of claim 10, wherein the angle is selected such that neitherthe excitation beam, nor the outgoing signal light, intercepts thecoverslip.
 13. The microscope of claim 1, wherein the signal light has awavelength of λ/2.
 14. The microscope of claim 1, wherein the signallight is generated though a non-linear signal generation process. 15.The microscope of claim 1, wherein the signal light includesfluorescence light emitted from the sample after excitation by theBessel-like beam.
 16. The microscope of claim 1, further comprising anannular mask in a path of the light beam configured to generate anannular ring of light from which the Bessel-like beam is formed.
 17. Amicroscope comprising: a light source for generating a light beam havinga wavelength, λ; beam-forming optics configured for receiving the lightbeam and generating a Bessel-like beam that is directed into a sample,the beam-forming optics including an excitation objective having an axisoriented in a first direction; imaging optics configured for receivinglight from a position within the sample that is illuminated by theBessel-like beam and for imaging the received light on a detector, theimaging optics including a detection objective having an axis orientedin a second direction that is non-parallel to the first direction; adetector configured for detecting light received by the imaging optics,wherein the detector includes a plurality of individual detection units;and a controller operably coupled to the detector and configured toselectively record image data from individual detection units that imageportions of the sample that are illuminated by a central lobe of theBessel-like beam while not recording data from individual detectionunits that image portions of the sample that are not illuminated by thecentral lobe of the Bessel-like beam; a processor configured to generatean image of the sample based on the selectively recorded image data thatis recorded from different positions of the Bessel beam within thesample.
 18. The microscope of claim 17, further comprising beam scanningoptics configured for scanning the Bessel-like beam within the sample ina direction having a component perpendicular to the first direction. 19.The microscope of claim 18, wherein the beam scanning optics areconfigured to scan the Bessel-like beam in the sample in steps that aregreater than or approximately equal to a corresponding spacing betweenneighboring individual detector elements in the detector.
 20. Themicroscope of claim 19, further comprising a beam blocking unitconfigured to block the Bessel-like beam from reaching the sample whenthe Bessel-like beam is scanned from one step position to a next stepposition.
 21. The microscope of claim 18, further comprising adiffractive optical element (DOE) configured to generate a plurality oflight beams from the light beam generated by the light source andwherein the beam-forming optics are configured for receiving theplurality of light beams and generating a plurality of Bessel-like beamsthat in the sample, the plurality of light beams being spaced from eachother by a spatial period that is greater than the diameter of a sidelobe of the Bessel-like beams; and wherein the imaging optics arefurther configured for simultaneously receiving light from positionswithin the sample that are illuminated by the plurality of Bessel-likebeams and for imaging the received light on the detector; and whereinthe controller is further configured to selectively record image datasimultaneously from individual detection units that image portions ofthe sample that are illuminated by a central lobe of the Bessel-likebeams while not recording data from individual detection units thatimage portions of the sample that are not illuminated by the centrallobes of the Bessel-like beams.
 22. The microscope of claim 21, whereinthe processor is configured to generate an image of the sample based onthe selectively recorded image data that is recorded from differentpositions of the Bessel beam within the sample, after the plurality ofBessel-like beams are scanned over the spatial period.
 23. Themicroscope of claim 17, wherein the Bessel-like beam has a ratio of aRayleigh length, z_(R) to a minimum beam waist, w_(o), of more than2πw_(o)/λ and less than 100πw_(o)/λ.
 24. The microscope of claim 17,wherein the Bessel-like beam has a non-zero ratio of a minimum numericalaperture to a maximum numerical aperture of less than 0.95.
 25. Themicroscope of claim 17, wherein the Bessel-like beam has a non-zeroratio of a minimum numerical aperture to a maximum numerical aperture ofless than 0.90.
 26. The microscope of claim 17, wherein the Bessel-likebeam has a minimum numerical aperture greater than zero and a ratio ofenergy in a first side of the beam to energy in the central lobe of thebeam of less than 0.5.
 27. The microscope of claim 17, furthercomprising a coverslip that supports the sample, wherein a normaldirection to a plane of the sample that supports the sample forms andangle with the first direction of more than 10 degrees and less than 80degrees.
 28. The microscope of claim 27, wherein the sample is less thanten micrometers thick.
 29. The microscope of claim 17, furthercomprising an annular mask in a path of the light beam configured togenerate an annular ring of light from which the Bessel-like beam isformed.
 30. A microscope comprising: a light source for generating alight beam having a wavelength, λ; beam-forming optics, including anoptical element positioned in a path of the light beam and configuredfor generating an annular ring of light, the beam-forming optics beingconfigured for generating from the light beam an excitation beam havinga central lobe and at least one side lobe and also configured to directthe excitation beam to a position within a sample, wherein thebeam-forming optics include an excitation objective having an axisoriented in a first direction, and wherein a transverse profile of theexcitation beam in the sample is intermediate between a profile of alowest order Bessel function and the Gaussian function; imaging opticsconfigured for receiving light from a position within the sample that isilluminated by the excitation beam and for imaging the received light ona detector, the imaging optics including a detection objective having anaxis oriented in a second direction that is non-parallel to the firstdirection; and a detector configured for detecting light received by theimaging optics.
 31. The microscope of claim 30, wherein the opticalelement positioned in a path of the light beam and configured forgenerating an annular ring of light includes an annular apodizationmask.
 32. The microscope of claim 30, wherein the optical elementpositioned in a path of the light beam and configured for generating anannular ring of light includes a binary phase mask.
 33. The microscopeof claim 30, wherein the optical element positioned in a path of thelight beam and configured for generating an annular ring of lightincludes a programmable spatial light modulator.
 34. The microscope ofclaim 30, wherein the excitation beam has a non-zero minimum numericalaperture and a maximum numerical aperture, and a ratio between theminimum numerical aperture and the maximum numerical aperture is lessthan about 0.95.
 35. The microscope of claim 30, wherein the excitationbeam has a non-zero minimum numerical aperture and a maximum numericalaperture, and a ratio between the minimum numerical aperture and themaximum numerical aperture is less than about 0.90.
 36. The microscopeof claim 30, wherein an amount of energy in a highest-energy side lobeof the excitation beam is less than about half of an amount of energy inthe central lobe of the excitation beam.
 37. The microscope of claim 30,wherein a ratio of a Rayleigh length, z_(R), of the excitation beam inthe sample to a minimum beam waist, w_(o), of the excitation beam in thesample is more than about 2πw_(o)/λ and less than about 100πw_(o)/λ. 38.The microscope of claim 30, further comprising a cover slip having aplanar surface upon which the sample is mounted or cultured, the planarsurface being tilted at an angle between 10 and 80 degrees with respectto the first direction.
 39. The microscope of claim 38, wherein thesample is less than ten micrometers thick.
 40. The microscope of claim30, further comprising beam scanning optics configured for scanning theexcitation beam in a direction having a component perpendicular to thefirst direction.
 41. The microscope of claim 30, wherein the signallight is generated though a non-linear signal generation process. 42.The microscope of claim 30, wherein the signal light includesfluorescence light emitted from the sample after excitation by theBessel-like beam.
 43. A microscope comprising: a light source forgenerating a light beam having a wavelength, λ; beam-forming opticsconfigured for receiving the light beam and generating a Bessel-likebeam that is directed into a sample, the beam-forming optics includingan excitation objective having a numerical aperture (NA) and an axisoriented in a first direction; imaging optics configured for receivingsignal light from a position within the sample that is illuminated bythe Bessel-like beam and for imaging the received light on a detector,the imaging optics including a detection objective having an axisoriented in a second direction that is non-parallel to the firstdirection; beam-translation optics configured for translating theposition of the Bessel-like beam within the sample in discrete steps ofmore than or about λ/2NA to create a first excitation pattern ofmultiple Bessel-like beams having a spatial period, Λ, equal to thedistance between beam positions of neighboring steps and configured tocreate N-1 additional excitation patterns that are spatially phaseshifted from the first excitation pattern by (N-1)Λ/N; a detectorconfigured for detecting signal light received by the imaging optics,the detector having individual detection units; and a processorconfigured to generate N images from the received signal light, each nimage, for n=1 to N, being based on detected light due to excitation ofthe sample by the n^(th) excitation pattern and further configuredgenerate a final image of the sample through a linear combination of theN individual images.
 44. The microscope of claim 43, wherein generatingthe final image of the sample through a linear combination of the Nindividual images, includes combining the individual images according to$I_{final} = {{{\sum\limits_{n = 1}^{N}{I_{n}{\exp \left( {2{{{\pi }n}/N}} \right)}}}}.}$45. The microscope of claim 43, wherein the signal light has awavelength of λ/2.
 46. The microscope of claim 43, wherein the signallight is generated though a non-linear signal generation process. 47.The microscope of claim 43, wherein N=3.
 48. The microscope of claim 43,wherein the step size is less than or about λ/NA.
 49. The microscope ofclaim 43, wherein N≧5.
 50. The microscope of claim 49, wherein the stepsize is greater than or about λ/NA.
 51. The microscope of claim 43,wherein the Bessel-like beam has a ratio of a Rayleigh length, z_(R) toa minimum beam waist, w_(o), of more than 2πw_(o)/λ and less than100πw_(o)/λ.
 52. The microscope of claim 43, wherein the Bessel-likebeam has a non-zero ratio of a minimum numerical aperture to a maximumnumerical aperture of less than 0.95.
 53. The microscope of claim 43,wherein the Bessel-like beam has a non-zero ratio of a minimum numericalaperture to a maximum numerical aperture of less than 0.90.
 54. Themicroscope of claim 43, wherein the Bessel-like beam has a minimumnumerical aperture greater than zero and a ratio of energy in a firstside of the beam to energy in the central lobe of the beam of less than0.5.
 55. The microscope of claim 43, further comprising a coverslip thatsupports the sample, wherein a normal direction to a plane of the samplethat supports the sample forms and angle with the first direction ofmore than 10 degrees and less than 80 degrees.
 56. The microscope ofclaim 55, wherein the sample is less than ten micrometers thick.
 57. Themicroscope of claim 43, further comprising an annular mask in a path ofthe light beam configured to generate an annular ring of light fromwhich the Bessel-like beam is formed.
 58. A microscope comprising: alight source for generating a light beam having a wavelength, λ;beam-forming optics, including an optical element positioned in a pathof the light beam and configured for generating an annular ring oflight, the beam-forming optics being configured for generating from thelight beam an excitation beam having a central lobe and at least oneside lobe and also configured to direct the excitation beam to aposition within a sample, wherein the beam-forming optics include anexcitation objective having an axis oriented in a first direction, andwherein a transverse profile of the excitation beam in the sample isintermediate between a profile of a lowest order Bessel function and theGaussian function; imaging optics configured for receiving signal lightfrom a position within the sample that is illuminated by the excitationbeam and for imaging the received light on a detector, the imagingoptics including a detection objective having an axis oriented in asecond direction that is non-parallel to the first direction, whereinthe signal light is generated though a non-linear signal generationprocess; and a detector configured for detecting the signal lightreceived by the imaging optics.
 59. The microscope of claim 58, furthercomprising beam scanning optics configured for scanning the Bessel-likebeam in a direction having a component perpendicular to the firstdirection.
 60. The microscope of claim 58, wherein the Bessel-like beamhas a ratio of a Rayleigh length, z_(R) to a minimum beam waist, w_(o),of more than 2πw_(o)/λ and less than 100πw_(o)/λ.
 61. The microscope ofclaim 58, wherein the Bessel-like beam has a non-zero ratio of a minimumnumerical aperture to a maximum numerical aperture of less than 0.95.62. The microscope of claim 58, wherein the Bessel-like beam has anon-zero ratio of a minimum numerical aperture to a maximum numericalaperture of less than 0.90.
 63. The microscope of claim 58, wherein theBessel-like beam has a minimum numerical aperture greater than zero anda ratio of energy in a first side lobe of the beam to energy in thecentral lobe of the beam of less than 0.5.
 64. The microscope of claim58, further comprising a coverslip that supports the sample, wherein anormal direction to a plane of the sample that supports the sample formsan angle with the first direction of more than 10 degrees and less than80 degrees.
 65. The microscope of claim 64, wherein the sample is lessthan ten micrometers thick.
 66. The microscope of claim 64, wherein theangle is selected such that neither the excitation beam, nor theoutgoing signal light, intercepts the coverslip.
 67. The microscope ofclaim 64, wherein the signal light has a wavelength of λ/2.
 68. Themicroscope of claim 64, wherein the signal light includes fluorescencelight emitted from the sample after excitation by the Bessel-like beam.69. The microscope of claim 64, further comprising an annular mask in apath of the light beam configured to generate an annular ring of lightfrom which the Bessel-like beam is formed.
 70. A microscope comprising:a light source for generating a light beam having a wavelength, λ; firstbeam-forming optics configured for receiving the light beam andgenerating a first Bessel-like beam that is directed into a sample, thebeam-forming optics including a first excitation objective having anumerical aperture (NA_(EO)) and an axis oriented in a first direction;imaging optics configured for receiving signal light from a positionwithin the sample that is illuminated by the first Bessel-like beam andfor imaging the received light on a detector, the imaging opticsincluding a detection objective having a numerical aperture (NA_(DO))and an axis oriented in a second direction that is non-parallel to thefirst direction; first beam-translation optics configured fortranslating the position of the first Bessel-like beam within the samplein discrete steps of more than or about λ/2NA_(EO) to create a firstexcitation pattern of multiple first Bessel-like beams having a spatialperiod, Λ, equal to the distance between beam positions of neighboringsteps and configured to create N-1 additional excitation patterns thatare spatially phase shifted from the first excitation pattern by(N-1)Λ/N; a detector configured for detecting first signal lightreceived by the imaging optics, the first signal light being emittedbased an interaction of the first Bessel-like beam with the sample, thedetector having individual detection units; and a processor configuredto: generate a real space constituent image for each of the N excitationpatterns; Fourier transform each of the real space constituent images togenerate reciprocal space constituent images for each of the excitationpatterns; combine the reciprocal space constituent images to generate afinal reciprocal space image; and re-transform the final reciprocalspace image to generate a final real space image of the sample, whereinthe final real space image of the sample has a resolution of less thatλ/2NA_(DO) in a coordinate orthogonal to the first direction.
 71. Themicroscope of claim 70, wherein the signal light has a wavelength ofλ/2.
 72. The microscope of claim 70, wherein the signal light isgenerated though a non-linear signal generation process.
 73. Themicroscope of claim 70, wherein N=3.
 74. The microscope of claim 73,wherein the step size is less than or about λ/NA_(EO).
 75. Themicroscope of claim 73, wherein N≧5.
 76. The microscope of claim 75,wherein the step size is greater than or about λ/NA_(EO).
 77. Themicroscope of claim 70, wherein the first Bessel-like beam has a ratioof a Rayleigh length, z_(R) to a minimum beam waist, w_(o), of more than2πw_(o)/λ and less than 100πw_(o)/λ.
 78. The microscope of claim 70,wherein the first Bessel-like beam has a non-zero ratio of a minimumnumerical aperture to a maximum numerical aperture of less than 0.95.79. The microscope of claim 70, wherein the first Bessel-like beam has anon-zero ratio of a minimum numerical aperture to a maximum numericalaperture of less than 0.90.
 80. The microscope of claim 70, wherein thefirst Bessel-like beam has a minimum numerical aperture greater thanzero and a ratio of energy in a first side of the beam to energy in thecentral lobe of the beam of less than 0.5.
 81. The microscope of claim70, further comprising a coverslip that supports the sample, wherein anormal direction to a plane of the sample that supports the sample formsand angle with the first direction of more than 10 degrees and less than80 degrees.
 82. The microscope of claim 81, wherein the sample is lessthan ten micrometers thick.
 83. The microscope of claim 70, furthercomprising an annular mask in a path of the light beam configured togenerate an annular ring of light from which the first Bessel-like beamis formed.
 84. The microscope of claim 70, further comprising secondbeam-forming optics configured for receiving a light beam having awavelength λ′ and generating a second Bessel-like beam that is directedinto the sample, the second beam-forming optics including a secondexcitation objective having a numerical aperture (NA′_(EO)) and an axisoriented in a third direction that is not parallel to the firstdirection and not parallel to the second direction, wherein the imagingoptics are further configured for receiving second signal light from aposition within the sample that is illuminated by the second Bessel-likebeam and for imaging the received second signal light on the detector;second beam-translation optics configured for translating the positionof the second Bessel-like beam within the sample in discrete steps ofmore than or about λ′/2NA′_(EO) to create a first excitation pattern ofmultiple second Bessel-like beams having a spatial period, Λ′, equal tothe distance between beam positions of neighboring steps and configuredto create N′-1 additional excitation patterns of multiple secondBessel-like beams that are spatially phase shifted from the firstexcitation pattern by (N′-1)Λ′/N′; wherein the detector is furtherconfigured for detecting second signal light received by the imagingoptics, the second signal light being emitted based an interaction ofthe second Bessel-like beam with the sample; and wherein the processoris further configured to: generate a real space constituent image foreach of the N′ excitation patterns; Fourier transform each of the realspace constituent images to generate reciprocal space constituent imagesfor each of the excitation patterns; combine the reciprocal spaceconstituent images to generate a final reciprocal space image; andre-transform the final reciprocal space image to generate a final realspace image of the sample, wherein the final real space image of thesample has a resolution of less that λ′/2NA_(DO) in a coordinateorthogonal to the second direction.
 85. The microscope of claim 84,wherein λ′=λ.
 86. The microscope of claim 84, wherein N′=3.
 87. Themicroscope of claim 86, wherein the step size is less than or aboutλ′/NA′_(EO).
 88. The microscope of claim 84, wherein the secondBessel-like beam has a ratio of a Rayleigh length, z_(R) to a minimumbeam waist, w_(o), of more than 2πw_(o)/λ′ and less than 100πw_(o)/λ′.89. The microscope of claim 84, wherein the second Bessel-like beam hasa non-zero ratio of a minimum numerical aperture to a maximum numericalaperture of less than 0.95.
 90. The microscope of claim 84, wherein thesecond Bessel-like beam has a non-zero ratio of a minimum numericalaperture to a maximum numerical aperture of less than 0.90.
 91. Themicroscope of claim 84, wherein the second Bessel-like beam has aminimum numerical aperture greater than zero and a ratio of energy in afirst side of the beam to energy in the central lobe of the beam of lessthan 0.5.